Polynomial Operations

Polynomial Operations

There are four main polynomial operations which are:

  • Addition of Polynomials
  • Subtraction of Polynomials
  • Multiplication of Polynomials
  • Division of Polynomials

Each of the operations on polynomials is explained below using solved examples.

Addition of Polynomials

To add polynomials, always add the like terms, i.e. the terms having the same variable and power. The addition of polynomials always results in a polynomial of the same degree. 

Subtraction of Polynomials

Subtracting polynomials is similar to addition, the only difference being the type of operation. So, subtract the like terms to obtain the solution. It should be noted that subtraction of polynomials also results in a polynomial of the same degree.

Multiplication of Polynomials

Two or more polynomial when multiplied always result in a polynomial of higher degree (unless one of them is a constant polynomial).

Division of Polynomials

Division of two polynomial may or may not result in a polynomial. Let us study below the division of polynomials in detail. To divide polynomials, follow the given steps:

Polynomial Division Steps:

If a polynomial has more than one term, we use long division method for the same. Following are the steps for it.

  1. Write the polynomial in descending order.
  2. Check the highest power and divide the terms by the same.
  3. Use the answer in step 2 as the division symbol.
  4. Now subtract it and bring down the next term.
  5. Repeat steps 2 to 4 until you have no more terms to carry down.
  6. Note the final answer, including remainder, will be in the fraction form (last subtract term).